1
REDUCE LATEX Formula Interface
( RLFI )
Ver. 1.1 05/91
Richard Liska, Ladislav Drska
Computational Physics Group
Faculty of Nuclear Sciences and Physical Engineering
Czech Technical University in Prague
Brehova 7, 115 19 Prague 1, Czechoslovakia
E-mail: tjerl@cspuni12.bitnet
High quality typesetting of mathematical formulas is a quite tedious
task. One of the most sophisticated typesetting programs for
mathematical text TEX [1], together with its widely used macro package
LATEX [2], has a strange syntax of mathematical formulas, especially
of the complicated type. This is the main reason which lead us to
designing the formula interface between the computer algebra system
REDUCE [3] and the document preparation system LATEX. The other
reason is that all available syntaxes of the REDUCE formula output are
line oriented and thus not suitable for typesetting in mathematical
text. The idea of interfacing a computer algebra system to a
typesetting program has already been used, eg. in [4] presenting the
TeX output of the MACSYMA computer algebra system.
The formula interface presented here adds to REDUCE the new syntax of
formula output, namely LATEX syntax, and can also be named REDUCE -
LATEX translator. Text generated by REDUCE in this syntax can be
directly used in LATEX source documents. Various mathematical
constructions are supported by the interface including subscripts,
superscripts, font changing, Greek letters, divide-bars, integral and
sum signs, derivatives etc.
The interface can be used in two ways:
- for typesetting of results of REDUCE algebraic calculations.
- for typesetting of users formulas.
The latter can even be used by users unfamiliar with the REDUCE
system, because the REDUCE input syntax of formulas is almost the same
as the syntax of the majority of programming languages. We aimed at
speeding up the process of formula typesetting, because we are
convinced, that the writing of correct complicated formulas in the
REDUCE syntax is a much more simpler task than writing them in the
LATEX syntax full of keywords and special characters \, {, ^ etc. It
is clear, that not every formula produced by the interface is
typeset in the best format from an aesthetic point of view. When a
user is not satisfied with the result, he can add some LATEX commands
to the REDUCE output - LATEX input.
The interface is connected to REDUCE by three new switches and several
statements. To activate the LATEX output mode the switch LATEX must
be set ON. This switch, similar to the switch FORT producing FORTRAN
1output, being ON causes all outputs to be written in the LATEX syntax
of formulas. The switch VERBATIM is used for input printing control.
If it is ON input to REDUCE system is typesetted in LATEX verbatim
environment.
The switch LASIMP controls the algebraic evaluation of input formulas.
If it is ON every formula is evaluated, simplified and written in the
form given by ordinary REDUCE statements and switches such as FACTOR,
ORDER, RAT etc. In the case when the LASIMP switch is OFF evaluation,
simplification or reordering of formulas is not performed and REDUCE
acts only as a formula parser and the form of the formula output is
exactly the same as that of the input, the only difference remains in
the syntax. The mode OFF LASIMP is designed especially for
typesetting of formulas for which the user needs preservation of their
structure. This switch has no meaning if the switch LATEX is OFF and
thus is working only for LATEX output.
For every identifier used in the typesetted REDUCE formula the
following properties can be defined by the statement DEFID:
- its printing symbol (Greek letters can be used).
- the font in which the symbol will be typesetted.
- accent which will be typesetted above the symbol.
Symbols with indexes are treated in REDUCE as operators. Each index
corresponds to an argument of the operator. The meaning of operator
arguments (where one wants to typeset them) is declared by the
statement DEFINDEX. This statement causes the arguments to be
typesetted as subscripts or superscripts (on left or right-hand side
of the operator) or as arguments of the operator.
Statement mathstyle defines the style of formula typesetting.
Variable LALINE!* defines the length of output lines.
The fractions with horizontal divide bars are typesetted by using the
new REDUCE infix operator \. This operator is not algebraically
simplified. During typesetting of powers the checking on the form of
the power base and exponent is performed to determine the form of the
typesetted expression (eg. sqrt symbol, using parentheses).
Some special forms can be typeset by using REDUCE prefix operators.
These are as follows:
- INT - integral of an expression.
- DINT - definite integral of an expression.
- DF - derivative of an expression.
- PDF - partial derivative of an expression.
- SUM - sum of expressions.
- PRODUCT - product of expressions.
- SQRT - square root of expression.
There are still some problems unsolved in the present version of the
interface as follows:
- breaking the formulas which do not fit on one line.
- automatic decision where to use divide bars in fractions.
- distinction of two- or more-character identifiers from the product of
one-character symbols.
- typesetting of matrices.
Description of files
RLFI.RED - REDUCE source file for this interface, file RLFI in the
test file RLFI.TST
RLFI.DOC - this document
RLFI.TST - test file for this interface
RLFI.LOG - LATEX output of the test session, file TEX in the test
file RLFI.TST, can be directly used as LATEX input file.
Remark
After finishing presented interface, we have found another work [5],
which solves the same problem. The RLFI package has been described in
[6] too.
References
[1] D.E. Knuth, The TeX book (Addison-Wesley, Reading, 1984).
[2] L. Lamport, LATEX A Document Preparation System (Addison-Wesley,
Reading 1986).
[3] A.C. Hearn, REDUCE User's Manual, Ver 3.4 (The RAND Corporation,
Santa Monica 1991).
[4] J.R. Fateman, ACM SIGSAM Bulletin 21 (1987) 4.
[5] W. Antweiler, A. Strotmann and V. Winkelmann, ACM SIGSAM Bulletin
23 (1989) 26.
[6] L. Drska, R. Liska, M. Sinor, Two practical packages for
computational physics - GCPM, RLFI, Comp. Phys. Comm., 61,
(1990), 225 - 230.
APPENDIX: Summary and syntax
Warning
The RLFI package can be used only on systems supporting lower case
letters with OFF RAISE statement. The package distinquishes the
upper and lower case letters, so be carefull in typing them.
Switches
LATEX - If ON output is in LATEX format. It turns OFF the RAISE
switch if it is set ON and ON the RAISE switch if set OFF.
It turns OFF resp. ON the RAISE switch when turned ON resp.
OFF. By default is OFF.
LASIMP - If ON formulas are evaluated (simplified), REDUCE works
as usually. If OFF no evaluation is performed and the structure
of formulas is preserved. By default is ON.
VERBATIM - If ON REDUCE input, while LATEX switch being ON, is
printed in LATEX verbatim environment. It turns ON resp. OFF the
ECHO switch when turned ON resp. OFF. By default is ON.
Operators
infix - \
1prefix - INT,DINT,DF,PDF,SUM,PRODUCT,SQRT
<alg. expression> \ <alg. expression>
INT(<function>,<variable>)
DINT(<from>,<to>,<function>,<variable>)
DF(<function>,<variables>)
<variables> ::= <o-variable>|<o-variable>,<variables>
<o-variable> ::= <variable>|<variable>,<order>
<variable> ::= <kernel>
<order> ::= <integer>
<function> ::= <alg. expression>
<from> ::= <alg. expression>
<to> ::= <alg. expression>
PDF(<function>,<variables>)
SUM(<from>,<to>,<function>)
PRODUCT(<from>,<to>,<function>)
SQRT(<alg. expression>)
<alg. expression> is any algebraic expression. Where appropriate, it
can include also relational operators (e.g. argument <from> of SUM or
PRODUCT operators is usually equation). <kernel> is identifier or
prefix operator with arguments as described in [3].
Statements
MATHSTYLE <m-style>;
<m-style> ::= math | displaymath | equation
DEFID <identifier>,<d-equations>;
<d-equations> ::= <d-equation> | <d-equation>,<d-equations>
<d-equation> ::= <d-print symbol> | <d-font>|<d-accent>
<d-print symbol> ::= NAME = <print symbol>
<d-font> ::= FONT = <font>
<d-accent> ::= ACCENT = <accent>
<print symbol> ::= <character> | <special symbol>
<special symbol> ::= alpha|beta|gamma|delta|epsilon|varepsilon|zeta|
eta|theta|vartheta|iota|kappa|lambda|mu|nu|xi|pi|varpi|rho|
varrho|sigma|varsigma|tau|upsilon|phi|varphi|chi|psi|omega|
Gamma|Delta|Theta|Lambda|Xi|Pi|Sigma|Upsilon|Phi|Psi|Omega|
infty|hbar (see [2] p.43,45)
<font> ::= bold|roman
<accent> ::=hat|check|breve|acute|grave|tilde|bar|vec|dot|ddot
(see [2] p.51)
DEFINDEX <d-operators>;
<d-operators> ::= <d-operator> | <d-operator>,<d-operators>
<d-operator> ::= <prefix operator>(<descriptions>)
<prefix operator> ::= <identifier>
<descriptions> ::= <description> | <description>,<descriptions>
<description> ::= ARG | UP | DOWN | LEFTUP | LEFTDOWN
The meaning of the statements is briefly described in the preceding text.